%I A151282
%S A151282 1,2,6,18,58,190,638,2170,7474,25974,90982,320738,1137002,4049838,14485326,
               52001290,187292514,
%T A151282 676546790,2450311862,8895769714,32366225562,117995832990,430960312862,
               1576675041434,
%U A151282 5777325893266,21200338220630,77901645076998,286615385651970,1055762834791114,
               3893279267979662
%N A151282 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,
               0) and consisting of n steps taken from {(-1, -1), (-1, 0), (0, 1), 
               (1, 1)}
%C A151282 Contribution from Paul Barry (pbarry(AT)wit.ie), Jan 19 2009: (Start)
%C A151282 Hankel transform is 2^C(n+1,2).
%C A151282 Row sums of Riordan array ((1-2x)/(1-x+2x^2),x(1-x)/(1-x+2x^2))^{-1}.
%C A151282 G.f.: 1/(1-2x-2x^2/(1-x-2x^2/(1-x-2x^2/(1-x-2x^2/(1-.... (continued fraction).
%C A151282 First column of Riordan array ((1-x)/(1+x+2x^2),x/(1+x+2x^2))^{-1}. (End)
%H A151282 M. Bouquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter 
               plane, <a href="http://arxiv.org/abs/0810.4387">ArXiv 0810.4387</
               a>.
%H A151282 A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted 
               Lattice Walks, <a href="http://arxiv.org/abs/0811.2899">ArXiv 0811.2899</
               a>.
%t A151282 aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, 
               j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = 
               aux[-1 + i, -1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, 
               j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[i, j, n], 
               {i, 0, n}, {j, 0, n}], {n, 0, 25}]
%Y A151282 Sequence in context: A148459 A081057 A000137 this_sequence A157004 A085139 
               A150041
%Y A151282 Adjacent sequences: A151279 A151280 A151281 this_sequence A151283 A151284 
               A151285
%K A151282 nonn,walk
%O A151282 0,2
%A A151282 Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008